ALBERT LEON WHITEMAN MEMORIAL MATHEMATICS LECTURES
Whiteman Lecturer: Dr. Alexander Lubotzky (Hebrew University)
January 22 & 24, 2008
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Dr. Lubotzky will deliver two lectures
Tuesday, January 22, 2008
3:30 pm - 4:30 pm
Reception: Davidson Conference Center Club Room
4:30 pm - 5:30 pm
General Lecture:
Short Presentations of Finite Simple Groups
Location: Davidson Conference Center Club Room
5:30 pm - 7:00 pm
Cocktails and Dinner
Location: Davidson Conference Center Vineyard Room
Thursday, January 24, 2008
2:00 pm - 3:00 pm
Specialized Lecture:
Hyperbolic Manifolds and Finite groups
Location: Kaprielian Hall, Room 249
Abstract - Short Presentations of Finite Simple Groups
Finding 'nice & compact' presentations of various groups has been a subject of great interest for groups theorists for more than a century. Well known presentations are the Coxeter presentation of the finite symmetric groups and Steinberg presentation of groups of Lie type. In response to conjectures of Babai and Szemeredi on one hand (motivated by questions in computational group theory) and of Mann on the other hand (motivated by questions on subgroup growth) we show that all non-abelian finite simple groups (with the possible exception of Ree groups) have presentations which are small (bounded number of relations) and short (w.r.t the length of the relations). This is very surprising as the simple abelian groups- the cyclic groups of prime order- do not have such presentations! We will describe the motivations and results, a cohomological application (proving a conjecture of Holt) and some connections with discrete subgroups of Lie groups and topology.
Abstract - Hyperbolic Manifolds and Finite Groups
The isometry group of a closed hyperbolic n-manifold is finite. We prove that for every n>1 and every finite group G there is an n-dimensional closed hyperbolic manifold whose isometry group is G. This resolves a long standing problem whose low dimensional cases n=2 and n=3 were proved by Greenberg ('74) and Kojima ('88) resp. The proof is nonconstructive; it uses a 'probabilistic method', i.e. counting results from the theory of 'subgroup growth'. The talk will not assume any prior knowledge on the subject.
Dr. Alexander Lubotzky
Alex Lubotzky has been at the Hebrew University since 1982 and is currently the holder of the Maurice and Clara Weil Chair in Mathematics. He has also been a member of the Yale faculty since 2003. His visiting positions include the Eilenberg Visiting Professorship at Columbia, Stanford, Chicago and the Institute for Advanced Study, where he recently led a year long program in Groups, representations and discrete mathematics. He served in the Israeli Knesset from 1996-1999. He is a fellow of the AAAs and was recently awarded an honorary degree from the University of Chicago. he has won the Bergman Memorial Prize, the Endos Prize and the Rothschild Prize.
Lubotzky is one of the leading researchers in algebraic and lie groups and their discrete subgroups, arithmetic groups, combinatorial and computational group theory and its applications to graph theory, computer science, geometry and number theory. He is the author of more than 100 articles and 4 books.
Albert Leon Whiteman
The Albert L. Whiteman Memorial Mathematics Lectures were established by his wife Sally Whiteman and is supported by gifts from other family members, his colleagues, students and friends. Professor Whiteman is distinguished by his research in number theory and combinatorics and his nearly 50 years of service to USC. The University is privileged to honor the memory of Professor Whiteman with an annual lecture by an eminent mathematician.
For dinner reservation and more information, please contact Amy Yung (
amy@usc.edu), (213) 740-81768
